Question

find the length of the third side. if necessary, write in simplest radical form.

Explanation:

Step1: Recall Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c=10$, $a=4$, solve for $b$.

Step2: Rearrange to solve for unknown side

$b^2 = c^2 - a^2$

Step3: Substitute given values

$b^2 = 10^2 - 4^2 = 100 - 16 = 84$

Step4: Simplify the radical

$b = \sqrt{84} = \sqrt{4 \times 21} = 2\sqrt{21}$

Answer:

$2\sqrt{21}$